A068896 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A068896

Primes containing 2k digits in which the sum of the first k digits is that of the last k digits.

11, 1423, 1607, 1753, 1973, 2011, 2213, 2341, 2543, 2617, 2671, 2819, 2837, 3407, 3461, 3517, 3571, 3719, 3847, 4013, 4637, 4673, 4691, 4729, 4783, 4967, 5023, 5261, 5519, 5573, 5591, 5647, 5683, 5849, 5867, 6143, 6217, 6271, 6473, 6491, 6529, 6547, 7043, 7649, 7759, 8017, 8053, 8219, 8237, 8273, 8291, 8329, 8677, 9137, 9173, 9283, 9467

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

2341 is a member with 2+3 = 4+1.

MATHEMATICA

Select[Prime[Range[169, 1229]], Length[Union[Total/@TakeDrop[ IntegerDigits[ #], 2]]] == 1&] (* The program generates all 56 4-digit terms. To generate all 3669 of the 6-digit terms, change the Range constants to (9593, 78498) and change the 2 to 3. *) (* Harvey P. Dale, Aug 15 2021 *)

PROG

(Python)

from sympy import primerange

def sd(s): return sum(map(int, s))

def auptod(digits):

alst = []

for d in range(2, digits+1, 2):

for p in primerange(10**(d-1), 10**d):

s = str(p)

if sd(s[:len(s)//2]) == sd(s[len(s)//2:]): alst.append(p)

return alst

print(auptod(4)) # Michael S. Branicky, Aug 15 2021